SPM short course SPM short course

Functional integration and connectivityFunctional integration and connectivitySPM short course SPM short course

Functional integration and connectivityFunctional integration and connectivity

Christian BüchelChristian Büchel

Karl FristonKarl Friston

The Wellcome Department of Cognitive Neurology, UCLThe Wellcome Department of Cognitive Neurology, UCL

London UK http//:www.fil.ion.ucl.ac.uk/spmLondon UK http//:www.fil.ion.ucl.ac.uk/spm

Data analysisData analysis

RealignmentRealignment SmoothingSmoothing

NormalisationNormalisation

General linear modelGeneral linear model

fMRI time-seriesfMRI time-series

Parameter estimatesParameter estimates

Design matrixDesign matrix

TemplateTemplate

KernelKernel

p <0.05p <0.05

Inference with Gaussian Inference with Gaussian field theoryfield theory

Adjusted regional dataAdjusted regional data

spatial modes and spatial modes and effective connectivityeffective connectivity

Functional brain architecturesFunctional brain architecturesFunctional brain architecturesFunctional brain architectures

Functional segregationFunctional segregationUnivariate analyses of regionally Univariate analyses of regionally specific effectsspecific effects

Functional segregationFunctional segregationUnivariate analyses of regionally Univariate analyses of regionally specific effectsspecific effects

Functional integrationFunctional integrationMultivariate analyses of Multivariate analyses of regional interactionsregional interactions

Functional integrationFunctional integrationMultivariate analyses of Multivariate analyses of regional interactionsregional interactions

Functional connectivityFunctional connectivity““the temporal correlation between the temporal correlation between neurophysiological events”neurophysiological events”

an operational definitionan operational definition

Functional connectivityFunctional connectivity““the temporal correlation between the temporal correlation between neurophysiological events”neurophysiological events”

an operational definitionan operational definition

Effective connectivityEffective connectivity““the influence one neuronal system the influence one neuronal system exerts over another”exerts over another”

a model-dependent definitiona model-dependent definition

Effective connectivityEffective connectivity““the influence one neuronal system the influence one neuronal system exerts over another”exerts over another”

a model-dependent definitiona model-dependent definition

Issues in functional integrationIssues in functional integrationIssues in functional integrationIssues in functional integration

• Functional ConnectivityFunctional ConnectivityEigenimage analysis and PCAEigenimage analysis and PCA

• Effective ConnectivityEffective ConnectivityPsychophysiological InteractionsPsychophysiological InteractionsState space Models (Variable parameter regression)State space Models (Variable parameter regression)Structural Equation ModellingStructural Equation ModellingVolterra seriesVolterra series

Effective vs. functional connectivityEffective vs. functional connectivityEffective vs. functional connectivityEffective vs. functional connectivity

Model: A = V1 fMRI time-seriesB = 0.5 * A + e1C = 0.3 * A + e2

Model: A = V1 fMRI time-seriesB = 0.5 * A + e1C = 0.3 * A + e2

Correlations:

A B C10.49 10.30 0.12 1

Correlations:

A B C10.49 10.30 0.12 1

A

B

C

0.49

0.31

-0.02

2=0.5, ns.

Correct model

Correct model

Eigenimages - the basic conceptEigenimages - the basic conceptEigenimages - the basic conceptEigenimages - the basic concept

A time-series of 1D imagesA time-series of 1D images128 scans of 40 “voxels”128 scans of 40 “voxels”

Expression of 1st 3 “eigenimages”Expression of 1st 3 “eigenimages”

Eigenvalues and spatial “modes”Eigenvalues and spatial “modes”

The time-series ‘reconstituted’The time-series ‘reconstituted’

Eigenimages and SVDEigenimages and SVDEigenimages and SVDEigenimages and SVD

Y Y (DATA)(DATA)

timetime

voxelsvoxels

Y = USVY = USVTT = = ss11UU11VV11TT + + ss22UU22VV22

T T + ... + ...

APPROX. APPROX. OF YOF Y

UU11

==APPROX. APPROX.

OF YOF YAPPROX. APPROX.

OF YOF Y

+ + ss22 + + ss33 + ...+ ...ss11

UU22 UU33

VV11 VV22 VV33

An example from PETAn example from PETAn example from PETAn example from PET

Eigenimage analysis of aEigenimage analysis of aPET word generation studyPET word generation study

Word generation Word generation GGWord repetitionWord repetition RR

R G R G R G.........R G R G R G.........

Dynamic changes in effective connectivityDynamic changes in effective connectivity Attentional modulation of V5 responses to visual motionAttentional modulation of V5 responses to visual motion

Dynamic changes in effective connectivityDynamic changes in effective connectivity Attentional modulation of V5 responses to visual motionAttentional modulation of V5 responses to visual motion

• Psychophysiological interactionsPsychophysiological interactions

Attentional modulation of V2 to V5 connectionsAttentional modulation of V2 to V5 connections

• State space models and variable parameter regressionState space models and variable parameter regressionAttentional modulation of V5 to PPC connectionsAttentional modulation of V5 to PPC connections

• Models of effective connectivityModels of effective connectivity

The mediating role of posterior parietal cortexThe mediating role of posterior parietal cortex

in attentional modulationin attentional modulation

Structural Equation modellingStructural Equation modelling

Volterra formulationVolterra formulation

The fMRI studyThe fMRI study

StimuliStimuli

250 radially moving dots at 4.7 degrees/s250 radially moving dots at 4.7 degrees/s

Pre-ScanningPre-Scanning

5 x 30s trials with 5 speed changes (reducing to 1%)5 x 30s trials with 5 speed changes (reducing to 1%)

Task - detect change in radial velocityTask - detect change in radial velocity

Scanning (no speed changes)Scanning (no speed changes)

6 normal subjects, 4 100 scan sessions;6 normal subjects, 4 100 scan sessions;

each session comprising 10 scans of 4 different conditioneach session comprising 10 scans of 4 different condition

e.g. F A F N F A F N S .................e.g. F A F N F A F N S .................

F - fixation point onlyF - fixation point only

A - motion stimuli with attention (detect changes)A - motion stimuli with attention (detect changes)

N - motion stimuli without attentionN - motion stimuli without attention

S - no motionS - no motion

PsychophysiologicalPsychophysiological interactions:interactions:

Attentional modulation ofAttentional modulation ofV2 -> V5 influencesV2 -> V5 influences

AttentionAttention

V2V2

V5V5

attention

no attention

V2 activity

V5

acti

vity

SPM{Z}

time

V5

acti

vity

Regression with time-varying coefficientsRegression with time-varying coefficients

Fixed regression model (one coefficient for entire time-series)Fixed regression model (one coefficient for entire time-series)

y = x*b + ey = x*b + e

Time varying regression model (coefficient changes over time) Time varying regression model (coefficient changes over time)

yyt t = x= xtt..bbtt + e + ett

bbtt = b = bt-1t-1+h+htt

Coefficient b of the explanatory variable (V5) is modelledCoefficient b of the explanatory variable (V5) is modelled

as a time-varying random walk. Estimation by Kalman filter.as a time-varying random walk. Estimation by Kalman filter.

AttentionFixation No attention

bbtt

x = V5x = V5y = PPy = PP

Time (scans)regr

essi

on c

oeff

icie

nt0.5

0.8

The source of modulatory afferentsThe source of modulatory afferentsThe source of modulatory afferentsThe source of modulatory afferents

p<0.05 correctedp<0.05 corrected

RR

RR

““Modulatory” sources Modulatory” sources identified as regions identified as regions correlated with correlated with bbtt

Anterior cingulate Dorsolateral prefrontal cortexAnterior cingulate Dorsolateral prefrontal cortex

Minimise the difference between the observed (Minimise the difference between the observed (SS) and implied () and implied () covariances by adjusting the path ) covariances by adjusting the path coefficients (a, b, c) coefficients (a, b, c)

The implied covariance structure: The implied covariance structure:

xx = x.B + z= x.B + zxx = z.(I - B)= z.(I - B)-1-1

x : matrix of time-series of regions U, V and Wx : matrix of time-series of regions U, V and W

B: matrix of unidirectional path coefficients (a,b,c)B: matrix of unidirectional path coefficients (a,b,c)

Variance-covariance structure:Variance-covariance structure:

xxT T . x = . x = = (I-B)= (I-B)-T-T. C.(I-B). C.(I-B)-1-1

where Cwhere C = z= zTT z z

xxTT.x is the implied variance covariance structure .x is the implied variance covariance structure C contains the residual variances (u,v,w) and covariancesC contains the residual variances (u,v,w) and covariances

The free parameters are estimated by minimising a [maximum likelihood] function of The free parameters are estimated by minimising a [maximum likelihood] function of SS and and

Structural equation modelling (SEM)Structural equation modelling (SEM)Structural equation modelling (SEM)Structural equation modelling (SEM)

U

W

Va

bc

u v

w

Attention - No attentionAttention - No attentionAttention - No attentionAttention - No attention

AttentionNo attention

0.760.47

0.750.43

PPPP

==

The use of moderator or interaction variablesThe use of moderator or interaction variablesThe use of moderator or interaction variablesThe use of moderator or interaction variables

V5V5

V1V1

V1xPPV1xPP

V5V5

2 =11, p<0.01

0.14

Modulatory influence of parietal cortex on V1 to V5Modulatory influence of parietal cortex on V1 to V5

Hierarchical architecturesHierarchical architecturesHierarchical architecturesHierarchical architectures

V1V1

V5V5PPPP

PFCPFC

LGNLGN

22=13.6, p<0.01=13.6, p<0.01

22=5.9, p<0.01=5.9, p<0.010.1

0.2

Changes in effective connectivity over time: LearningChanges in effective connectivity over time: Learning Changes in effective connectivity over time: LearningChanges in effective connectivity over time: Learning

• Paired associates learningPaired associates learning

• Pairing Pairing – Object (Snodgrass) withObject (Snodgrass) with

– LocationLocation

• fMRI, 48 axial slices, TR 4.1s, 8 scans/condfMRI, 48 axial slices, TR 4.1s, 8 scans/cond

• 8 cycles (E)ncoding (C)ontrol (R)etrieval8 cycles (E)ncoding (C)ontrol (R)etrieval

• 3 sessions (each with new objects & locations)3 sessions (each with new objects & locations)

C C C

E R E R

V1

ITp ITaPP

LP

V1

ITp

DE

SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late SEM: Encoding Early vs. Late

V1

DE

PPLP

ITpITa

Early

0.57

0.45

0.35

0.15

0.410.61

-0.03

V1

DE

PPLP

ITpITa

Late

0.46

0.38

0.27

0.26

0.370.59

0.132 =6.3p<0.05diff. = 0.16

Single subjects: +0.27*, +0.21, +0.37*, +0.24*, +0.19, +0.31*

* p < 0.05

Changes in effective connectivity Changes in effective connectivity predict learningpredict learning

Changes in effective connectivity Changes in effective connectivity predict learningpredict learning

Length of EARLY (in learning blocks) that maximised the EARLY vs. LATE difference in connectivity (PP -> ITP)

lear

nin

g r

ate

k

r = 0.64

1

0.4

1 2 3 4 5 6 7

learning block

k = .35 k = .60

k = .63 k=.95

k = .71k =.44

% c

orr

ect

Volterra series - Volterra series - a general nonlinear input-output modela general nonlinear input-output model

y(t)y(t) = = 11[u(t)] + [u(t)] + 22[u(t)] + .... + [u(t)] + .... + nn[u(t)] + ....[u(t)] + ....

nn[u(t)] = [u(t)] = .... .... h hnn(t(t11,..., t,..., tnn)u(t - t)u(t - t11) .... u(t - t) .... u(t - tnn)d t)d t1 1 .... d t.... d tnn

[u(t)] response y(t)response y(t)input[s] u(t)input[s] u(t)

kernels (h)kernels (h)

Regional activitiesRegional activities

estimateestimate

Volterra series approximationVolterra series approximationVolterra series approximationVolterra series approximation

• Trying to explain activity in region Trying to explain activity in region AA by by

– past and present activity in other regions (1st order)past and present activity in other regions (1st order)

• direct effects (eg. effect of B on direct effects (eg. effect of B on AA))

– past and present activity in other regions (pairwise = 2nd order)past and present activity in other regions (pairwise = 2nd order)

• non-linear (eg. effect of Bnon-linear (eg. effect of B22 on on AA))

• modulatory (eg. effect of AB on modulatory (eg. effect of AB on AA) )

– AA = a = a11B + aB + a22C + aC + a33AA + aAA + a44BB + aBB + a55CC + aCC + a66AB + aAB + a77AC + aAC + a88BCBC

– All terms can be seen as regressors and their impact can be tested with the general linear All terms can be seen as regressors and their impact can be tested with the general linear modelmodel

– directdirect effect of B on effect of B on AA : B and BB as covariates of interests, others confounds : B and BB as covariates of interests, others confounds

– modulatorymodulatory effect of B on effect of B on AA : AB and BC as covariates of interest, others confounds : AB and BC as covariates of interest, others confounds

V3aV3a

PPCPPC

FEFFEF

V5V5

IFSIFS

PPCPPC

V5V5

PulPul

V1/V2V1/V2

PPCPPC

areas showing attentional effectsareas showing attentional effects

regional interactions examinedregional interactions examined

Changes in V5 response to V2 Changes in V5 response to V2 inputs with PPC activityinputs with PPC activity

i.e. a modulatory (activity-dependent)i.e. a modulatory (activity-dependent)component of V5 responsescomponent of V5 responses

SPM{F}

PPC activity = 1

PPC activity = 0